Electronic structure of donor states under a strong magnetic field

The electronic structures of quantum dots with 6, 9, and 13 electrons under the influence of a strong magnetic field together with a positive impurity has been studied. By diagonalizing the Hamiltonian and by a detailed analysis of the wave functions, both crystal-like and liquidlike states were found. The crystal-like states have clear core-ring structures. The effect of impurity and the effect of symmetry constraint on these structures has been clarified. Based on the symmetry constraint, the states can be well classified, and the candidates of magic angular momenta can be predicted.

Figure 1

$\epsilon \left(L\right)$ (in meV) as a function of $L$ with $N=6$, $B=10\mathrm{T}$, and $Z=1$ (a and b) or $Z=0$ (c). The LLL limitation is imposed in (a), but not in (b) and (c). In the two latter cases the number of the basis function is 12 000.

Figure 2

${\rho }_1\left(r\right)$ of the first states as a function of $r$. $N=6$, $B=10\mathrm{T}$ and $Z=1$ are given. The labels of state ${\left(L\right)}_1$ are marked in the subfigures.

Figure 3

Contour diagrams of ${\rho }_2({\mathbf{r}}_1,{\mathbf{r}}_2)$ as a function of ${\mathbf{r}}_1$ plotted in the upper half $X\text{−}Y$ plane. ${\mathbf{r}}_2$ is fixed and is marked by a black spot at the $X$ axis. $N=6$, $B=10\mathrm{T}$, and $Z=1$ are given. The darker area is larger in magnitude. The labels of state ${\left(L\right)}_1$ are marked.

Figure 4

The same as Fig. 3 but for $N=9$.

Figure 5

The same as Fig. 1b but for $N=9$ (a) and for $N=13$ (b). Each figure has a group of specific types.

Figure 6

The same as Fig. 3 but for $N=13$.

Figure 7

The three-body densities ${\rho }_3({\mathbf{r}}_1,{\mathbf{r}}_2,{\mathbf{r}}_3)$ as a function of ${\mathbf{r}}_1$ for $N=13$ dots. The given ${\mathbf{r}}_2$ and ${\mathbf{r}}_3$ are marked by two black spots. The darker area is associated with a larger ${\rho }_3$. $B=10\mathrm{T}$ and $Z=1$ are assumed.